Nuprl Lemma : rtermSubtract?_wf
∀[v:rat_term()]. (rtermSubtract?(v) ∈ 𝔹)
Proof
Definitions occuring in Statement :
rtermSubtract?: rtermSubtract?(v)
,
rat_term: rat_term()
,
bool: 𝔹
,
uall: ∀[x:A]. B[x]
,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x]
,
member: t ∈ T
,
ext-eq: A ≡ B
,
and: P ∧ Q
,
subtype_rel: A ⊆r B
,
all: ∀x:A. B[x]
,
implies: P
⇒ Q
,
bool: 𝔹
,
unit: Unit
,
it: ⋅
,
btrue: tt
,
uiff: uiff(P;Q)
,
uimplies: b supposing a
,
sq_type: SQType(T)
,
guard: {T}
,
eq_atom: x =a y
,
ifthenelse: if b then t else f fi
,
rtermConstant: "const"
,
rtermSubtract?: rtermSubtract?(v)
,
pi1: fst(t)
,
bfalse: ff
,
exists: ∃x:A. B[x]
,
or: P ∨ Q
,
bnot: ¬bb
,
assert: ↑b
,
false: False
,
rtermVar: rtermVar(var)
,
rtermAdd: left "+" right
,
rtermSubtract: left "-" right
,
rtermMultiply: left "*" right
,
rtermDivide: num "/" denom
,
rtermMinus: rtermMinus(num)
Lemmas referenced :
rat_term-ext,
eq_atom_wf,
eqtt_to_assert,
assert_of_eq_atom,
subtype_base_sq,
atom_subtype_base,
bfalse_wf,
eqff_to_assert,
bool_cases_sqequal,
bool_wf,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_atom,
btrue_wf,
rat_term_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
introduction,
extract_by_obid,
promote_hyp,
sqequalHypSubstitution,
productElimination,
thin,
hypothesis_subsumption,
hypothesis,
hypothesisEquality,
applyEquality,
sqequalRule,
isectElimination,
tokenEquality,
inhabitedIsType,
lambdaFormation_alt,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
independent_isectElimination,
instantiate,
cumulativity,
atomEquality,
dependent_functionElimination,
independent_functionElimination,
because_Cache,
dependent_pairFormation_alt,
equalityIstype,
voidElimination,
universeIsType
Latex:
\mforall{}[v:rat\_term()]. (rtermSubtract?(v) \mmember{} \mBbbB{})
Date html generated:
2019_10_29-AM-09_28_35
Last ObjectModification:
2019_03_31-PM-05_24_48
Theory : reals
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