Nuprl Lemma : minus-minus-sq
∀x:Top. (--x ~ x + 0)
Proof
Definitions occuring in Statement :
top: Top,
all: ∀x:A. B[x],
add: n + m,
minus: -n,
natural_number: $n,
sqequal: s ~ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
has-value: (a)↓,
member: t ∈ T,
implies: P ⇒ Q,
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
and: P ∧ Q,
squash: ↓T,
prop: ℙ,
subtype_rel: A ⊆r B,
true: True,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
top: Top,
false: False
Lemmas referenced :
value-type-has-value,
int-value-type,
has-value_wf_base,
is-exception_wf,
minus-minus,
sqle_wf_base,
squash_wf,
true_wf,
istype-base,
add-comm,
int_subtype_base,
subtype_rel_self,
iff_weakening_equal,
zero-add-sqle,
istype-void,
exception-not-value,
istype-top,
add-zero
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :lambdaFormation_alt,
cut,
sqequalRule,
thin,
sqequalSqle,
divergentSqle,
callbyvalueMinus,
sqequalHypSubstitution,
hypothesis,
baseApply,
closedConclusion,
baseClosed,
hypothesisEquality,
equalityTransitivity,
equalitySymmetry,
Error :inhabitedIsType,
introduction,
extract_by_obid,
isectElimination,
intEquality,
independent_isectElimination,
Error :equalityIstype,
dependent_functionElimination,
independent_functionElimination,
minusExceptionCases,
axiomSqleEquality,
exceptionSqequal,
sqleReflexivity,
because_Cache,
callbyvalueAdd,
productElimination,
applyEquality,
Error :lambdaEquality_alt,
imageElimination,
Error :universeIsType,
natural_numberEquality,
imageMemberEquality,
instantiate,
universeEquality,
Error :isect_memberEquality_alt,
voidElimination,
addExceptionCases
Latex:
\mforall{}x:Top. (--x \msim{} x + 0)
Date html generated:
2019_06_20-AM-11_22_18
Last ObjectModification:
2019_05_21-PM-11_00_48
Theory : arithmetic
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