Nuprl Lemma : bool_ind
∀[P:𝔹 ⟶ ℙ]. (P[ff] ⇒ P[tt] ⇒ {∀b:𝔹. P[b]})
Proof
Definitions occuring in Statement :
bfalse: ff,
btrue: tt,
bool: 𝔹,
uall: ∀[x:A]. B[x],
prop: ℙ,
guard: {T},
so_apply: x[s],
all: ∀x:A. B[x],
implies: P ⇒ Q,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
guard: {T},
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
all: ∀x:A. B[x],
member: t ∈ T,
prop: ℙ,
so_apply: x[s],
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
bfalse: ff
Lemmas referenced :
bool_wf,
btrue_wf,
bfalse_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
Error :isect_memberFormation_alt,
lambdaFormation,
cut,
introduction,
extract_by_obid,
hypothesis,
applyEquality,
hypothesisEquality,
Error :functionIsType,
Error :universeIsType,
universeEquality,
sqequalHypSubstitution,
unionElimination,
thin,
equalityElimination
Latex:
\mforall{}[P:\mBbbB{} {}\mrightarrow{} \mBbbP{}]. (P[ff] {}\mRightarrow{} P[tt] {}\mRightarrow{} \{\mforall{}b:\mBbbB{}. P[b]\})
Date html generated:
2019_06_20-AM-11_31_18
Last ObjectModification:
2018_09_26-AM-11_16_09
Theory : bool_1
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