Nuprl Lemma : qexp2
∀[q:ℚ]. (q ↑ 2 = (q * q) ∈ ℚ)
Proof
Definitions occuring in Statement :
qexp: r ↑ n,
qmul: r * s,
rationals: ℚ,
uall: ∀[x:A]. B[x],
natural_number: $n,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
squash: ↓T,
prop: ℙ,
nat_plus: ℕ+,
less_than: a < b,
less_than': less_than'(a;b),
true: True,
and: P ∧ Q,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
subtract: n - m
Lemmas referenced :
equal_wf,
squash_wf,
true_wf,
rationals_wf,
exp_unroll_q,
less_than_wf,
qmul_wf,
iff_weakening_equal,
qexp1
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
cut,
applyEquality,
thin,
lambdaEquality,
sqequalHypSubstitution,
imageElimination,
introduction,
extract_by_obid,
isectElimination,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
universeEquality,
dependent_set_memberEquality,
natural_numberEquality,
sqequalRule,
independent_pairFormation,
imageMemberEquality,
baseClosed,
because_Cache,
independent_isectElimination,
productElimination,
independent_functionElimination
Latex:
\mforall{}[q:\mBbbQ{}]. (q \muparrow{} 2 = (q * q))
Date html generated:
2018_05_22-AM-00_00_51
Last ObjectModification:
2017_07_26-PM-06_49_42
Theory : rationals
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