Nuprl Lemma : decidable__int_equal
∀i,j:ℤ. Dec(i = j ∈ ℤ)
Proof
Definitions occuring in Statement :
decidable: Dec(P),
all: ∀x:A. B[x],
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
decidable: Dec(P),
member: t ∈ T,
or: P ∨ Q,
uall: ∀[x:A]. B[x],
prop: ℙ,
false: False,
implies: P ⇒ Q,
not: ¬A,
subtype_rel: A ⊆r B
Lemmas referenced :
less-trichotomy,
not_wf,
equal-wf-base,
int_subtype_base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
intEquality,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
unionElimination,
int_eqEquality,
inlEquality,
axiomEquality,
hypothesis,
isectElimination,
because_Cache,
inrEquality,
sqequalRule,
lambdaEquality,
independent_functionElimination,
voidElimination,
applyEquality
Latex:
\mforall{}i,j:\mBbbZ{}. Dec(i = j)
Date html generated:
2019_06_20-AM-11_22_56
Last ObjectModification:
2018_08_17-AM-11_32_11
Theory : arithmetic
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