Nuprl Lemma : eq_int_eq_false_elim
∀[i,j:ℤ]. i ≠ j supposing (i =z j) = ff
Proof
Definitions occuring in Statement :
eq_int: (i =z j),
bfalse: ff,
bool: 𝔹,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
nequal: a ≠ b ∈ T ,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
nequal: a ≠ b ∈ T ,
not: ¬A,
implies: P ⇒ Q,
false: False,
prop: ℙ,
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q
Lemmas referenced :
equal-wf-base,
int_subtype_base,
bool_wf,
decidable__int_equal,
eq_int_eq_true,
btrue_neq_bfalse
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
lambdaFormation,
thin,
sqequalHypSubstitution,
hypothesis,
independent_functionElimination,
voidElimination,
extract_by_obid,
isectElimination,
intEquality,
hypothesisEquality,
applyEquality,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
because_Cache,
Error :universeIsType,
baseApply,
closedConclusion,
baseClosed,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
Error :inhabitedIsType,
unionElimination,
independent_isectElimination
Latex:
\mforall{}[i,j:\mBbbZ{}]. i \mneq{} j supposing (i =\msubz{} j) = ff
Date html generated:
2019_06_20-AM-11_32_00
Last ObjectModification:
2018_09_26-AM-11_24_54
Theory : bool_1
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