Nuprl Lemma : not_zero_sqequal_one
(0 ~ 1) ⇒ False
Proof
Definitions occuring in Statement :
implies: P ⇒ Q,
false: False,
natural_number: $n,
sqequal: s ~ t
Definitions unfolded in proof :
implies: P ⇒ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
sq_type: SQType(T),
all: ∀x:A. B[x],
guard: {T},
true: True,
false: False
Lemmas referenced :
subtype_base_sq,
int_subtype_base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
sqequalRule,
hypothesis,
natural_numberEquality,
thin,
instantiate,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
cumulativity,
intEquality,
independent_isectElimination,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
voidElimination,
promote_hyp,
sqequalIntensionalEquality
Latex:
(0 \msim{} 1) {}\mRightarrow{} False
Date html generated:
2016_05_13-PM-03_19_57
Last ObjectModification:
2015_12_26-AM-09_09_19
Theory : sqequal_1
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