Nuprl Lemma : trivial-arith
(3 = 2 ∈ ℤ) ⇒ False
Proof
Definitions occuring in Statement :
implies: P ⇒ Q,
false: False,
natural_number: $n,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
implies: P ⇒ Q,
false: False,
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
sq_type: SQType(T),
all: ∀x:A. B[x],
guard: {T},
true: True,
prop: ℙ
Lemmas referenced :
subtype_base_sq,
int_subtype_base,
false_wf,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
hypothesis,
addLevel,
thin,
instantiate,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
cumulativity,
intEquality,
independent_isectElimination,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
natural_numberEquality,
voidElimination,
levelHypothesis,
promote_hyp
Latex:
(3 = 2) {}\mRightarrow{} False
Date html generated:
2016_05_13-PM-03_31_50
Last ObjectModification:
2015_12_26-AM-09_45_45
Theory : arithmetic
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